Least Squares Collocation Alternative to Helmert’s Transformation with Hausbrandt’s Post – Transformation Correction

Alternative transformation from Cartesian to geodetic coordinates by least squares for GPS georeferencing applications

The inverse transformation of coordinates, from Cartesian to curvilinear geodetic, or symbolically (x,y,z)-(l,j,h) has been extensively researched in the geodetic literature. However, published formulations require that the application must be deterministically implemented point-by-point individually. Recently, and thanks to GPS technology, scientists have made available thousands of determinat...

Least-Squares Estimation of Transformation Parameters Between Two Point Patterns

PEDOMODELS FITTING WITH FUZZY LEAST SQUARES REGRESSION

Pedomodels have become a popular topic in soil science and environmentalresearch. They are predictive functions of certain soil properties based on other easily orcheaply measured properties. The common method for fitting pedomodels is to use classicalregression analysis, based on the assumptions of data crispness and deterministic relationsamong variables. In modeling natural systems such as s...

تعیین ژئوئید محلی مناطق نفت خیز جنوب به روش least-squares collocation

به منظور دستیابی به بسیاری از اهداف ژئودزی، ژئوفیزیک، اقیانوس شناسی، اقلیم شناسی‍ و ... مقدار ارتفاع ژئویید همواره مورد نیاز است. بنابراین چگونگی محاسبه و تعیین هرچه دقیق تر این مقدار، از دیر باز از اهمیت بسیاری برخوردار بوده است. ژئویید یکی از سطوح هم پتانسیل زمین می باشد که به بهترین وجه سطح متوسط آب های آزاد (msl) را با نرم کمترین مربعات تقریب می نماید. تا کنون شیوه های بسیاری برای تعیین ارت...

A least-squares preconditioner for radial basis functions collocation methods

Although meshless radial basis function (RBF) methods applied to partial differential equations (PDEs) are not only simple to implement and enjoy exponential convergence rates as compared to standard mesh-based schemes, the system of equations required to find the expansion coefficients are typically badly conditioned and expensive using the global Gaussian elimination (G-GE) method requiring O...